Related papers: Is time the real line?
Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…
Confusion and disagreement around the notion of time is due to the fact that we often fail to recognize that we call 'time' a variety of distinct notions, only partially related to one another. Many apparently obvious properties of time are…
We give an exact mathematical construction of a spacelike order $<$, which is dual to the standard chronological order $\ll$ in the $n$-dimensional Minkowski space $M^n$, and we discuss its order-theoretic, geometrical as well as its…
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
Have our fundamental theories got time right? Does size really matter? Or is physics all in the eyes of the beholder? In this essay, we question the origin of time and scale by reevaluating the nature of measurement. We then argue for a…
How does the topological space of science emerge? Inspired by the concept of maps of science, i.e. mapping scientific topics to a scientific space, we ask which topological structure a dynamical process of authors collaborating and…
The existence of a thermodynamic arrow of time in the present universe implies that the initial state of the observable portion of our universe at (or near) the ``big bang'' must have been very ``special''. We argue that it is not plausible…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…
The direct and indirect experimental proofs of a strong time invariance violation in optics are discussed. Time noninvariance for present day becomes the only real physical base for explanation the origin of the most phenomena in nonlinear…
The topology of the causal boundary for standard static spacetimes--spacetimes time-invariantly conformal to a metric product of the Lorentz line and a Riemannian manifold--is studied in depth. As this is given in terms of a set of…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
Despite the fact that the fundamental physical laws are symmetric in time, most observed processes do not show this symmetry. Especially the phenomenon of decay seems to involve a kind of irreversibility that makes the definition of a…
It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields…
Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the…
The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval onto the unit square. From this fact one can easily construct of a continuous surjection from the real line…
In this paper it is presented the model of a multiverse made up of entangled pairs of universes. The arrow of time obtained from the principles of thermodynamics and the arrow of time given by the thermodynamics of entanglement for single…
We summarize the arguments that space and time are likely to be emergent notions; i.e. they are not present in the fundamental formulation of the theory, but appear as approximate macroscopic concepts. Along the way we briefly review…
We relate physical time with the topology of magnetic field vortices. We base ourselves on a formulation of unimodular gravity where the cosmological constant $\Lambda$ appears as the canonical dual to a variable which on-shell becomes…
One of the most fundamental questions of modern physics is the nature of spacetime. There are various propositions on the table, as the grand unified theory, quantum gravity, supersymmetry, string and superstring theories, and M theory.…
Milnor's fibration theorem is about the geometry and topology of real and complex analytic maps near their critical points, a ubiquitous theme in mathematics. As such, after 50 years, this has become a whole area of research on its own,…